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Frontiers of Mathematics in China

, Volume 14, Issue 2, pp 315–348 | Cite as

Conformal minimal immersions with constant curvature from S2 to Q5

  • Xiaoxiang Jiao
  • Hong LiEmail author
Research Article
  • 2 Downloads

Abstract

We study the geometry of conformal minimal two spheres immersed in G(2; 7; ℝ): Then we classify the linearly full irreducible conformal minimal immersions with constant curvature from S2 to G(2; 7; ℝ); or equivalently, a complex hyperquadric Q5 under some conditions. We also completely determine the Gaussian curvature of all linearly full totally unramified irreducible and all linearly full reducible conformal minimal immersions from S2 to G(2; 7; ℝ) with constant curvature. For reducible case, we give some examples, up to SO(7) equivalence, in which none of the spheres are congruent, with the same Gaussian curvature.

Keywords

Conformal minimal surface isotropy order constant curvature linearly full 

MSC

53C42 53C55 

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Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11871450)

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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